Properties Side Properties 1. All sides are congruent
Angle Properties 1. Consecutive angles are supplementary Example Proof
Prove: Angle HOm and Angle MOI are supplementary
Diagonal Properties 1. Diagonals bisect each other
2. *Diagonals bisect the angles
This is the most important property of a rhombus for the following reasons:
- Knowing that these diagonals bisect the angles, we can identify triangles (Triangle RHO, Triangle RMO, Triangle HOM, Triangle HRM) as isosceles, and use properties of isosceles to find unknown side and angle measures
- Knowing that these diagonals bisect the angles, congruence of oppositely oriented triangles can be proved using triangle congruence shortcuts
Rhombus is a kite with opposite parallel sides
Properties
Side Properties
1. All sides are congruent
Angle Properties
1. Consecutive angles are supplementary
Example Proof
Prove: Angle HOm and Angle MOI are supplementary
Diagonal Properties
1. Diagonals bisect each other
2. *Diagonals bisect the angles
This is the most important property of a rhombus for the following reasons:
- Knowing that these diagonals bisect the angles, we can identify triangles (Triangle RHO, Triangle RMO, Triangle HOM, Triangle HRM) as isosceles, and use properties of isosceles to find unknown side and angle measures
- Knowing that these diagonals bisect the angles, congruence of oppositely oriented triangles can be proved using triangle congruence shortcuts